Decision under risk 2 Flashcards
Define prospect theory
-Prospect theory generalises EUT to encoropate weighting and value finctions and a refernce level.
EUp = Σw(pi)V(y + xi – r)
-W(p) - weighting function
-V() - value functinon
-Reference level
Cancellation (Editing in PT)
-Removing of prospects that are shared by prospects
Segreagtion (Editing in PT)
-Segregating the riskless, guaranteed component from the risky prospoect/gabmle
Eg) (£300, 0.8; £200, 0.2) becomes the sure
amount £200 plus the prospect
(£100, 0.8; £0, 0.2)
Combination (Editing in PT)
-Process of simplyfying prospects by combining probabilites which are associated with identical outcomes.
-Eg) (100, 0.25: 100, 0.3: 50 , 0.45) becomes (100, 0.55: 50, 0.45)
Properties of the value function Prospect theory
-Looses are valued greater than gains, a £10 loss is pyshcologcaly worse than a 10 gain.
-Diminishing sensitivity which means slope of value function decreases as we move away from reference point. Implying risk averse over gains, risk loving over losses. The relfection effect explains diminishing sensitivity.
-Contains a reference point when V(0) = 0.
-Outcomes are judged in terms of losses and gains relative to reference point.
Weighting function properties
-w(0) = 0 and w(1) = 1
-Not defined close to 0 and 1
-Weighting functions are overweighting for small probabilites.
-Subcertainty, decision weights sum less to 1.
-Subproportionaliy meaning log w(p) is a convex function of log(p)
-Allais paradox implies subcertainty.
Proof of overweighting of the weighting function PT example
-PT argues for small probs weighting function leads to decisiion weights > P.
Eg)A: (£5000, 0.001; £0, 0.999), B: (£5, 1)
-Most people choose A
-V(x) = sqrt(x)
Define decision weights
Decision weights are used in measuring outcomes relative to R.
-Decision weights are not probabilities and are not observed directly instead are inferred from decisions regarding choices between prospects.
Violations of stochastic dominance in PT (direct and indirect effects) + if indirect effect is negative
-Violations occur when a prospect stochastically dominates another yet isnt chosen.
-Moving more p onto better outcome has two effect on EU:
-direct effect (always positive): refers to the prob weight on the good outcome increases.
-Indirect effect (can be either) refers to when the sum of the decision weights may either incresae or decrease relative to shift in prob from bad to good outcome.
-If indirect effect negative and outweights direct effect, stochastic dominance can be violted due to probabilty weighting.
example of overwighting
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